The crystal structures,electronic structures and optical properties of nitrogen or/and praseodymium doped anatase TiO_2 were calculated by first principles with the plane-wave ultrasoft pseudopotential method based on density functional theory.Highly efficient visible-light-induced nitrogen or/and praseodymium doped anatase TiO_2 nanocrystal photocatalyst were synthesized by a microwave chemical method.The calculated results show that the photocatalytic activity of TiO_2 can be enhanced by N doping or Pr doping,and can be further enhanced by N+Pr codoping.The band gap change of the codoping TiO_2 is more obvious than that of the single ion doping,which results in the red shift of the optical absorption edges.The results are of great significance for the understanding and further development of visible-light response high activity modified TiO_2 photocatalyst.The photocatalytic activity of the samples for methyl blue degradation was investigated under the irradiation of fluorescent light.The experimental results show that the codoping TiO_2 photocatalytic activity is obviously higher than that of the single ion doping.The experimental results accord with the calculated results.